package.json5

@@ -24,6 +24,7 @@
   },
   dependencies: {
     'bigint-isqrt': '^0.2.1',
+    'fraction.js': '^4.2.0',
     'typed-function': '^3.0.0',
   },
 }

pnpm-lock.yaml

@@ -2,11 +2,13 @@ lockfileVersion: 5.4
 
 specifiers:
   bigint-isqrt: ^0.2.1
+  fraction.js: ^4.2.0
   mocha: ^10.0.0
   typed-function: ^3.0.0
 
 dependencies:
   bigint-isqrt: 0.2.1
+  fraction.js: 4.2.0
   typed-function: 3.0.0
 
 devDependencies:
@@ -192,6 +194,10 @@ packages:
     hasBin: true
     dev: true
 
+  /fraction.js/4.2.0:
+    resolution: {integrity: sha512-MhLuK+2gUcnZe8ZHlaaINnQLl0xRIGRfcGk2yl8xoQAfHrSsL3rYu6FCmBdkdbhc9EPlwyGHewaRsvwRMJtAlA==}
+    dev: false
+
   /fs.realpath/1.0.0:
     resolution: {integrity: sha512-OO0pH2lK6a0hZnAdau5ItzHPI6pUlvI7jMVnxUQRtw4owF2wk8lOSabtGDCTP4Ggrg2MbGnWO9X8K1t4+fGMDw==}
     dev: true

src/core/PocomathInstance.mjs

@@ -263,6 +263,7 @@ export default class PocomathInstance {
     * @param {{test: any => bool,  // the predicate for the type
     *          from: Record<string, <that type> => <type name>> // conversions
     *          before: string[]  // lower priority types
+    *          refines: string   // The type this is a subtype of
     *        }} specification
     *
     * The second parameter of this function specifies the structure of the
@@ -711,7 +712,12 @@ export default class PocomathInstance {
                   if (argType === 'any') {
                      throw TypeError(
                         `In call to ${name}, incompatible template arguments: `
-                           + args.map(a => JSON.stringify(a)).join(', '))
+                        // + args.map(a => JSON.stringify(a)).join(', ')
+                        // unfortunately barfs on bigints. Need a better formatter
+                        // wish we could just use the one that console.log uses;
+                        // is that accessible somehow?
+                           + args.map(a => a.toString()).join(', ')
+                           + ' of types ' + argTypes.join(', ') + argType)
                   }
                   argTypes.push(argType)
                }
@@ -947,7 +953,7 @@ export default class PocomathInstance {
             } else {
                throw new Error(
                   'Implement inexact self-reference in typed-function for '
-                     + neededSig)
+                     + `${name}(${neededSig})`)
             }
          }
          const refs = imps[aSignature].builtRefs

src/generic/Types/adapted.mjs

@@ -0,0 +1,88 @@
+import PocomathInstance from '../../core/PocomathInstance.mjs'
+/* creates a PocomathInstance incorporating a new numeric type encapsulated
+ * as a class. (This instance can the be `install()ed` in another to add the
+ * type so created.)
+ *
+ * @param {string} name       The name of the new type
+ * @param {class} Thing       The class implementing the new type
+ * @param {object} overrides  Patches to the auto-generated adaptation
+ */
+export default function adapted(name, Thing, overrides) {
+   const thing = new PocomathInstance('Adapted Thing')
+   const test = overrides.isa || Thing.isa || (x => x instanceof Thing)
+   thing.installType(name, {
+      test,
+      from: overrides.from || {},
+      before: overrides.before || [],
+      refines: overrides.refines || undefined
+   })
+
+   // Build the operations for Thing
+   const operations = {}
+   // first a creator function, with name depending on the name of the thing:
+   const creatorName = overrides.creatorName || name.toLowerCase()
+   const creator = overrides[creatorName]
+      ? overrides[creatorName]('')
+      : Thing[creatorName]
+         ? (Thing[creatorName])
+         : ((...args) => new Thing(...args))
+   const defaultCreatorImps = {
+      '': () => () => creator(),
+      '...any': () => args => creator(...args)
+   }
+   defaultCreatorImps[name] = () => x => x // x.clone(x)?
+   operations[creatorName] = overrides[creatorName] || defaultCreatorImps
+
+   // We make the default instance, just as a place to check for methods
+   const instance = overrides.instance || creator()
+
+   // Now adapt the methods to typed-function:
+   const unaryOps = {
+      abs: 'abs',
+      ceiling: 'ceil',
+      floor: 'floor',
+      invert: 'inverse',
+      round: 'round',
+      sqrt: 'sqrt',
+      negate: 'neg'
+   }
+   const binaryOps = {
+      add: 'add',
+      compare: 'compare',
+      divide: 'div',
+      equalTT: 'equals',
+      gcd: 'gcd',
+      lcm: 'lcm',
+      mod: 'mod',
+      multiply: 'mul',
+      subtract: 'sub'
+   }
+   for (const [mathname, standardname] of Object.entries(unaryOps)) {
+      if (standardname in instance) {
+         operations[mathname] = {}
+         operations[mathname][name] = () => t => t[standardname]()
+      }
+   }
+   operations.zero = {}
+   operations.zero[name] = () => t => creator()
+   operations.one = {}
+   operations.one[name] = () => t => creator(1)
+   operations.conjugate = {}
+   operations.conjugate[name] = () => t => t // or t.clone() ??
+
+   const binarySignature = `${name},${name}`
+   for (const [mathname, standardname] of Object.entries(binaryOps)) {
+      if (standardname in instance) {
+         operations[mathname] = {}
+         operations[mathname][binarySignature] = () => (t,u) => t[standardname](u)
+      }
+   }
+   if ('operations' in overrides) {
+      Object.assign(operations, overrides.operations)
+   }
+
+   thing.install(operations)
+   return thing
+}
+
+export {adapted}

src/generic/abs.mjs

@@ -0,0 +1,7 @@
+export const abs = {
+   T: ({
+      'smaller(T,T)': lt,
+      'negate(T)': neg,
+      'zero(T)': zr
+   }) => t => (smaller(t, zr(t)) ? neg(t) : t)
+}

src/generic/absquare.mjs

@@ -0,0 +1,6 @@
+export const absquare = {
+   T: ({
+      'square(T)': sq,
+      'abs(T)': abval
+   }) => t => sq(abval(t))
+}

src/generic/all.mjs

@@ -1,2 +1,22 @@
+import {adapted} from './Types/adapted.mjs'
+import Fraction from 'fraction.js/bigfraction.js'
+
 export * from './arithmetic.mjs'
 export * from './relational.mjs'
+
+export const fraction = adapted('Fraction', Fraction, {
+   before: ['Complex'],
+   from: {number: n => new Fraction(n)},
+   operations: {
+      compare: {'Fraction,Fraction': () => (f,g) => new Fraction(f.compare(g))},
+      mod: {
+         'Fraction,Fraction': () => (n,d) => {
+            // patch for "mathematician's modulus"
+            // OK to use full public API of Fraction here
+            const fmod = n.mod(d)
+            if (fmod.s === -1n) return fmod.add(d.abs())
+            return fmod
+         }
+      }
+   }
+})

src/generic/arithmetic.mjs

@@ -2,14 +2,18 @@ import {reducingOperation} from './reducingOperation.mjs'
 
 export * from './Types/generic.mjs'
 
+export {abs} from './abs.mjs'
+export {absquare} from './absquare.mjs'
 export const add = reducingOperation
+export {divide} from './divide.mjs'
 export const gcd = reducingOperation
 export {identity} from './identity.mjs'
 export {lcm} from './lcm.mjs'
 export {mean} from './mean.mjs'
 export {mod} from './mod.mjs'
 export const multiply = reducingOperation
-export {divide} from './divide.mjs'
+export {quotient} from './quotient.mjs'
+export {roundquotient} from './roundquotient.mjs'
 export {sign} from './sign.mjs'
 export {sqrt} from './sqrt.mjs'
 export {square} from './square.mjs'

src/generic/quotient.mjs

@@ -0,0 +1,3 @@
+export const quotient = {
+    'T,T': ({'floor(T)': flr, 'divide(T,T)':div}) => (n,d) => flr(div(n,d))
+}

src/generic/relational.mjs

@@ -3,7 +3,8 @@ export const compare = {
 }
 
 export const isZero = {
-   'undefined': () => u => u === 0
+   'undefined': () => u => u === 0,
+   T: ({'equal(T,T)': eq, 'zero(T)': zr}) => t => eq(t, zr(t))
 }
 
 export const equal = {
@@ -33,18 +34,20 @@ export const unequal = {
 export const larger = {
    'T,T': ({
       'compare(T,T)': cmp,
-      'one(T)' : uno
+      'one(T)' : uno,
-   }) => (x,y) => cmp(x,y) === uno(y)
+      'equalTT(T,T)' : eq
+   }) => (x,y) => eq(cmp(x,y), uno(y))
 }
 
 export const largerEq = {
    'T,T': ({
       'compare(T,T)': cmp,
       'one(T)' : uno,
-      'isZero(T)' : isZ
+      'isZero(T)' : isZ,
+      'equalTT(T,T)': eq
    }) => (x,y) => {
       const c = cmp(x,y)
-      return isZ(c) || c === uno(y)
+      return isZ(c) || eq(c, uno(y))
    }
 }
 
@@ -52,16 +55,18 @@ export const smaller = {
    'T,T': ({
       'compare(T,T)': cmp,
       'one(T)' : uno,
-      'isZero(T)' : isZ
+      'isZero(T)' : isZ,
+      unequal
    }) => (x,y) => {
       const c = cmp(x,y)
-      return !isZ(c) && c !== uno(y)
+      return !isZ(c) && unequal(c, uno(y))
    }
 }
 
 export const smallerEq = {
    'T,T': ({
       'compare(T,T)': cmp,
-      'one(T)' : uno
+      'one(T)' : uno,
-   }) => (x,y) => cmp(x,y) !== uno(y)
+      unequal
+   }) => (x,y) => unequal(cmp(x,y), uno(y))
 }

src/generic/roundquotient.mjs

@@ -0,0 +1,3 @@
+export const roundquotient = {
+    'T,T': ({'round(T)': rnd, 'divide(T,T)':div}) => (n,d) => rnd(div(n,d))
+}

src/number/isZero.mjs

@@ -1,3 +1,6 @@
 export * from './Types/number.mjs'
 
-export const isZero = {number: () => n => n === 0}
+export const isZero = {
+    number: () => n => n === 0,
+    NumInt: () => n => n === 0  // necessary because of generic template
+}

src/number/quotient.mjs

@@ -1,8 +1,15 @@
 export * from './Types/number.mjs'
 
-export const quotient = {
+const intquotient = () => (n,d) => {
-   'number,number': () => (n,d) => {
+   if (d === 0) return d
-      if (d === 0) return d
+   return Math.floor(n/d)
-      return Math.floor(n/d)
+}
-   }
+
+export const quotient = {
+   // Hmmm, seem to need all of these because of the generic template version
+   // Should be a way around that
+   'NumInt,NumInt': intquotient,
+   'NumInt,number': intquotient,
+   'number,NumInt': intquotient,
+   'number,number': intquotient
 }

src/ops/floor.mjs

@@ -21,5 +21,10 @@ export const floor = {
 
    // OK to include a type totally not in Pocomath yet, it'll never be
    // activated.
-   Fraction: ({quotient}) => f => quotient(f.n, f.d),
+   // Fraction: ({quotient}) => f => quotient(f.n, f.d), // oops have that now
+   BigNumber: ({
+      'round(BigNumber)': rnd,
+      'equal(BigNumber,BigNumber)': eq
+   }) => x => eq(x,round(x)) ? round(x) : x.floor()
+
 }

test/generic/fraction.mjs

@@ -0,0 +1,95 @@
+import assert from 'assert'
+import math from '../../src/pocomath.mjs'
+import Fraction from 'fraction.js/bigfraction.js'
+
+describe('fraction', () => {
+   const half = new Fraction(1/2)
+   const tf = new Fraction(3, 4)
+   let zero // will fill in during a test
+   const one = new Fraction(1)
+
+   it('supports typeOf', () => {
+      assert.strictEqual(math.typeOf(half), 'Fraction')
+   })
+
+   it('can be built', () => {
+      zero = math.fraction()
+      assert.deepStrictEqual(zero, new Fraction(0))
+      assert.deepStrictEqual(math.fraction(1/2), half)
+      assert.strictEqual(math.fraction(half), half) // maybe it should be a clone?
+      assert.strictEqual(math.fraction(9, 16).valueOf(), 9/16)
+      assert.strictEqual(math.fraction(9n, 16n).valueOf(), 9/16)
+   })
+
+   it('has abs and sign', () => {
+      assert.deepStrictEqual(math.abs(math.fraction('-1/2')), half)
+      assert.deepStrictEqual(math.sign(math.negate(tf)), math.negate(one))
+   })
+
+   it('can add and multiply', () => {
+      assert.strictEqual(math.add(half, 1).valueOf(), 1.5)
+      assert.strictEqual(math.multiply(2, half).valueOf(), 1)
+   })
+
+   it('can subtract and divide', () => {
+      assert.strictEqual(math.subtract(half,tf).valueOf(), -0.25)
+      assert.strictEqual(math.divide(tf,half).valueOf(), 1.5)
+   })
+
+   it('computes mod', () => {
+      assert.strictEqual(math.mod(tf, half).valueOf(), 0.25)
+      assert.strictEqual(math.mod(tf, math.negate(half)).valueOf(), 0.25)
+      assert.strictEqual(math.mod(math.negate(tf), half).valueOf(), 0.25)
+      assert.strictEqual(
+         math.mod(math.negate(tf), math.negate(half)).valueOf(),
+         0.25)
+      assert.deepStrictEqual(
+         math.mod(math.fraction(-1, 3), half),
+         math.fraction(1, 6))
+   })
+
+   it('supports conjugate', () => {
+      assert.strictEqual(math.conjugate(half), half)
+   })
+
+   it('can compare fractions', () => {
+      assert.deepStrictEqual(math.compare(tf, half), one)
+      assert.strictEqual(math.equal(half, math.fraction("2/4")), true)
+      assert.strictEqual(math.smaller(half, tf), true)
+      assert.strictEqual(math.larger(half, tf), false)
+      assert.strictEqual(math.smallerEq(tf, math.fraction(0.75)), true)
+      assert.strictEqual(math.largerEq(tf, half), true)
+      assert.strictEqual(math.unequal(half, tf), true)
+      assert.strictEqual(math.isZero(math.zero(tf)), true)
+      assert.strictEqual(math.isZero(half), false)
+   })
+
+   it('computes gcd and lcm', () => {
+      assert.strictEqual(math.gcd(half,tf).valueOf(), 0.25)
+      assert.strictEqual(math.lcm(half,tf).valueOf(), 1.5)
+   })
+
+   it('computes additive and multiplicative inverses', () => {
+      assert.strictEqual(math.negate(half).valueOf(), -0.5)
+      assert.deepStrictEqual(math.invert(tf), math.fraction('4/3'))
+   })
+
+   it('computes integer parts and quotients', () => {
+      assert.deepStrictEqual(math.floor(tf), zero)
+      assert.deepStrictEqual(math.round(tf), one)
+      assert.deepStrictEqual(math.ceiling(half), one)
+      assert.deepStrictEqual(math.quotient(tf, half), one)
+      assert.deepStrictEqual(
+         math.roundquotient(math.fraction(7/8), half),
+         math.multiply(2,math.one(tf)))
+   })
+
+   it('has no sqrt (although that should be patched)', () => {
+      assert.throws(() => math.sqrt(math.fraction(9/16)), TypeError)
+   })
+
+   it('but it can square', () => {
+      assert.deepStrictEqual(math.square(tf), math.fraction(9/16))
+   })
+
+})